A Laguerre geometric approach to rational offsets

Branching blend of natural quadrics based on surfaces with rational offsets

A new branching blend between two natural quadrics (circular cylinders/cones or spheres) in many positions is proposed. The blend is a ring shaped patch of a PN surface (surface with rational offset) parametrized by rational bivariant functions of degree (6, 3). General theory of PN surfaces is developed using Laguerre geometry and a universal rational parametrization of the Blaschke cylinder. ...

Rational Offset Surfaces and Their Modeling Applications

This survey discusses rational surfaces with rational offset surfaces in Euclidean 3-space. These surfaces can be characterized by possessing a field of rational unit normal vectors, and are called Pythagorean normal surfaces. The procedure of offsetting curves and surfaces is present in most modern 3d-modeling tools. Since piecewise polynomial and rational surfaces are the standard representat...

PN-surfaces for blending applications

General theory of PN-surfaces (surfaces with rational offsets) is developed using dual Laguerre geometry and a universal rational parametrization of the Blaschke cylinder. This approach allows to construct new PN-blendings between two natural quadrics in many positions, and demostrate improved shape and lower parametrization degree than earlier proposed canal surface solutions. The construction...

Comparison between Rational Gegenbauer and Modified Generalized Laguerre Functions Collocation Methods for Solving the Case of Heat Transfer Equations Arising in Porous Medium

Smooth surface interpolation using patches with rational offsets

We present a new method for the interpolation of given data points and associated normals with surface parametric patches with rational normal fields. We give some arguments why a dual approach is the most convenient for these surfaces, which are traditionally called Pythagorean normal vector (PN) surfaces. Our construction is based on the isotropic model of the dual space to which the original...